Notes

1
Notes

• Assignment 3 on the web
• Due November 17
• Read a motion capture paper, write a report
• Final project on the web
• Dates
• November 12 (next Friday)Last day to finalize
  who is on your team and what you are doing (talk
  to me BEFORE then!)
• December 3 (last lecture)Code due. See PDF file
  on the website for what else you need to do or
  submit

2
Notes (2)

• Assignment 2 questions?
• Assignment 2 movies
• But dont take them off the web yet (TA needs to
  see them too -))

3
Morphing

• Before going further, lets take an aside into a
  2D animation technique morphing
• This will tie into 3D techniques later
• Basic idea
• We have two images (or video sequences) that we
  want to blend together
• But simply cross-dissolving looks bad unless the
  image features line up just right
• So as well as cross-dissolving, deform (warp)
  images to match features

4
Cross Dissolving

• Say we have two images, c1(x,y) and c2(x,y)
• Letting time t go from 0 to 1 (rescale to
  whatever you want) we define an intermediate
  image asc(x,y,t)(1-t)c1(x,y) t c2(x,y)
• More generally let c1 and c2 depend on time too
  (videos)
• More generally replace (1-t) and t with
  (1-f(x,y,t)) and f(x,y,t) for any appropriate
  function f
• E.g. dissolve part of the frame faster than
  another part

5
Warping

• If a feature appears in both images(e.g. eyes)
  but at different locations, then both are
  partially visible in intermediate frames of
  cross-dissolve
• We instead want features of first image to be
  replaced by features of second
• So figure out deformation that matches up the
  features
• Deform image 1 to d1(x,y)c1(warp1(x,y)) so that
  d1(x,y) and c2(x,y) have their features at the
  same (x,y) locations
• Deform image 2 to d2(x,y)c2(warp2(x,y))
  similarly
• Note maybe warp1 and warp2 are inverses

6
Defining a warp

• Dont want to have to specify where every pixel
  moves!
• Typical scenario
• Artist identifies features in image 1 and
  corresponding features in image 2
• Computer automatically fills in rest of warp in a
  smooth way
• Artist looks at result, adds more feature
  correspondences if unhappy
• Also of interest have computer figure out
  corresponding features automatically

7
Matching point features

• Simplest case (for computer) features are simply
  points
• Then its just a data interpolation problem find
  smooth warp(x,y) so that warp(xi,yi)(ui,vi) for
  each I
• (xi,yi) is the location of feature in one image
• (ui,vi) is the location in the other image
• Moving Least Squares (MLS)
• Radial Basis Functions (RBF)

8
Better features

• If all you have is points, artist needs to do a
  lot of work
• Silhouette must transform fairly exactly
• Other high contrast curves too (e.g. eye lids,
  lips, )
• So lots of points everywhere
• Worse need to get correspondence just right
  (dont mix up points, and get arclength
  parameters right)
• Editing correspondences is then painful
• Preferable to allow user to specify curves or at
  least line segments

9
Warping with line segments

• Textbook 3.8.2
• Features are line segments
• Define a rigid body scale transformation to
  follow segment
• Each point (x,y) gets mapped to some weighted
  average of where the transformations for each
  segment would take it
• Weight according to distance from segment

10
Problems

• What about crossing lines?
• Weird things may happen uninvertible maps,
  folding over,
• Lines not the ideal primitive for dealing with
  curvy image features